A worker develops a tension T in the cable as he attempts to move the 54-kg cart up the 18° incline. Determine the resulting acceleration a of the cart if (a) T = 142 N and (b) T = 208 N. Neglect all friction, except that at the worker's feet. The acceleration a is positive if up the slope, negative if down the slope. t 54 kg 11 Answers: 18° T
A worker develops a tension T in the cable as he attempts to move the 54-kg cart up the 18° incline. Determine the resulting acceleration a of the cart if (a) T = 142 N and (b) T = 208 N. Neglect all friction, except that at the worker's feet. The acceleration a is positive if up the slope, negative if down the slope. t 54 kg 11 Answers: 18° T
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Problem Statement
A worker develops a tension \( T \) in the cable as he attempts to move the 54-kg cart up the 18° incline. Determine the resulting acceleration \( a \) of the cart if:
- (a) \( T = 142 \, \text{N} \)
- (b) \( T = 208 \, \text{N} \)
Neglect all friction, except that at the worker's feet. The acceleration \( a \) is positive if up the slope, negative if down the slope.
### Diagram Explanation
The diagram provided illustrates a worker pulling a 54-kg cart up an 18° inclined plane using a cable that creates a tension \( T \):
- The tension \( T \) is represented by an arrow pointing along the direction of the cable.
- The cart with mass \( 54 \, \text{kg} \) sits on the inclined plane, and the angle of the incline is 18°.
- A smaller force component appied horizontally at the worker's feet is depicted but not quantified.
### Answers
To solve this problem, we will use Newton's second law \( F = ma \), where \( F \) is the net force acting on the cart and \( a \) is its acceleration.
#### Part (a): \( T = 142 \, \text{N} \)
\[ a = \left[ \boxed{} \right] \, \text{m/s}^2 \]
#### Part (b): \( T = 208 \, \text{N} \)
\[ a = \left[ \boxed{} \right] \, \text{m/s}^2 \]
The boxes next to each acceleration in the solution space are placeholders for students to input their answers after performing the calculations.
To complete the problems, apply the following steps:
1. Resolve the forces involved (tension \( T \), gravitational force \( mg \), and its components along the inclined plane).
2. Apply Newton’s second law in the direction along the incline.
3. Solve for the unknown acceleration \( a \) using the given values for \( T \).
### Educational Objective
This problem aims to teach students how to apply Newton's second law of motion to determine the acceleration of an object on an inclined plane, considering the tension in a cable and neglecting frictional forces except at the worker's feet. It also](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b7dd8f1-dbab-4607-8b33-bde9974f18c9%2Fdfb34e25-4e45-4932-99bc-e93bc303b0f2%2F0a3sdn_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A worker develops a tension \( T \) in the cable as he attempts to move the 54-kg cart up the 18° incline. Determine the resulting acceleration \( a \) of the cart if:
- (a) \( T = 142 \, \text{N} \)
- (b) \( T = 208 \, \text{N} \)
Neglect all friction, except that at the worker's feet. The acceleration \( a \) is positive if up the slope, negative if down the slope.
### Diagram Explanation
The diagram provided illustrates a worker pulling a 54-kg cart up an 18° inclined plane using a cable that creates a tension \( T \):
- The tension \( T \) is represented by an arrow pointing along the direction of the cable.
- The cart with mass \( 54 \, \text{kg} \) sits on the inclined plane, and the angle of the incline is 18°.
- A smaller force component appied horizontally at the worker's feet is depicted but not quantified.
### Answers
To solve this problem, we will use Newton's second law \( F = ma \), where \( F \) is the net force acting on the cart and \( a \) is its acceleration.
#### Part (a): \( T = 142 \, \text{N} \)
\[ a = \left[ \boxed{} \right] \, \text{m/s}^2 \]
#### Part (b): \( T = 208 \, \text{N} \)
\[ a = \left[ \boxed{} \right] \, \text{m/s}^2 \]
The boxes next to each acceleration in the solution space are placeholders for students to input their answers after performing the calculations.
To complete the problems, apply the following steps:
1. Resolve the forces involved (tension \( T \), gravitational force \( mg \), and its components along the inclined plane).
2. Apply Newton’s second law in the direction along the incline.
3. Solve for the unknown acceleration \( a \) using the given values for \( T \).
### Educational Objective
This problem aims to teach students how to apply Newton's second law of motion to determine the acceleration of an object on an inclined plane, considering the tension in a cable and neglecting frictional forces except at the worker's feet. It also
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